Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments
Correlations between grade and tonnage exist in mineral resource data compiled from published reports, but they are not always addressed during quantitative assessment of undiscovered mineral resources. Failure to account for correlated grade and tonnage distributions can result in geologically unre...
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Elsevier
2025-06-01
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| Series: | Applied Computing and Geosciences |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590197425000229 |
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| author | Joshua M. Rosera Graham W. Lederer John H. Schuenemeyer |
| author_facet | Joshua M. Rosera Graham W. Lederer John H. Schuenemeyer |
| author_sort | Joshua M. Rosera |
| collection | DOAJ |
| description | Correlations between grade and tonnage exist in mineral resource data compiled from published reports, but they are not always addressed during quantitative assessment of undiscovered mineral resources. Failure to account for correlated grade and tonnage distributions can result in geologically unrealistic assessment results. Current software tools simulate univariate ore tonnage and multivariate resource grades of undiscovered deposits independently. As a result, analysts are forced to rely on ad-hoc solutions to minimize the correlation issues by: 1) creating subsets of data with restricted criteria; 2) truncating grade and tonnage distributions; and 3) testing model robustness using exploratory data analysis. While these methods represent pragmatic solutions, the statistical solutions presented here provide additional options to address real correlations in grade and tonnage data used for mineral resource assessments. We present a modified version of the MapMark4 package in R that introduces two alternatives for modeling grade and tonnage distributions, consisting of a multivariate solution that accounts for correlations between ore tonnage and metal grades and an empirical solution that utilizes simple random sampling with replacement to reproduce coupled grades and tonnages from the input data. We present simulations for contained ore and metal for three case studies representing tungsten skarn, komatiite-hosted nickel, and sediment-hosted carbonate amagmatic zinc-lead (Mississippi Valley-type) deposits. Employing the methods presented here yields quantitative mineral resource assessment results that more closely reflect the empirical distributions of grades and tonnages observed in nature and expands the applicability of these tools for ongoing critical mineral resource assessments. |
| format | Article |
| id | doaj-art-b070b9bf85e448df926c65d8230ed9bb |
| institution | DOAJ |
| issn | 2590-1974 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Applied Computing and Geosciences |
| spelling | doaj-art-b070b9bf85e448df926c65d8230ed9bb2025-08-20T03:21:43ZengElsevierApplied Computing and Geosciences2590-19742025-06-012610024010.1016/j.acags.2025.100240Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessmentsJoshua M. Rosera0Graham W. Lederer1John H. Schuenemeyer2U.S. Geological Survey, Geology, Energy & Minerals Science Center, Reston, VA, USA; Corresponding author.U.S. Geological Survey, Geology, Energy & Minerals Science Center, Reston, VA, USASouthwest Statistical Consulting, LLC, USACorrelations between grade and tonnage exist in mineral resource data compiled from published reports, but they are not always addressed during quantitative assessment of undiscovered mineral resources. Failure to account for correlated grade and tonnage distributions can result in geologically unrealistic assessment results. Current software tools simulate univariate ore tonnage and multivariate resource grades of undiscovered deposits independently. As a result, analysts are forced to rely on ad-hoc solutions to minimize the correlation issues by: 1) creating subsets of data with restricted criteria; 2) truncating grade and tonnage distributions; and 3) testing model robustness using exploratory data analysis. While these methods represent pragmatic solutions, the statistical solutions presented here provide additional options to address real correlations in grade and tonnage data used for mineral resource assessments. We present a modified version of the MapMark4 package in R that introduces two alternatives for modeling grade and tonnage distributions, consisting of a multivariate solution that accounts for correlations between ore tonnage and metal grades and an empirical solution that utilizes simple random sampling with replacement to reproduce coupled grades and tonnages from the input data. We present simulations for contained ore and metal for three case studies representing tungsten skarn, komatiite-hosted nickel, and sediment-hosted carbonate amagmatic zinc-lead (Mississippi Valley-type) deposits. Employing the methods presented here yields quantitative mineral resource assessment results that more closely reflect the empirical distributions of grades and tonnages observed in nature and expands the applicability of these tools for ongoing critical mineral resource assessments.http://www.sciencedirect.com/science/article/pii/S2590197425000229Mineral resource assessmentsQuantitative assessmentsGrade and tonnage modelsMineral resourcesProbabilistic simulations |
| spellingShingle | Joshua M. Rosera Graham W. Lederer John H. Schuenemeyer Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments Applied Computing and Geosciences Mineral resource assessments Quantitative assessments Grade and tonnage models Mineral resources Probabilistic simulations |
| title | Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| title_full | Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| title_fullStr | Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| title_full_unstemmed | Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| title_short | Statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| title_sort | statistical approaches for modeling correlated grade and tonnage distributions and applications for mineral resource assessments |
| topic | Mineral resource assessments Quantitative assessments Grade and tonnage models Mineral resources Probabilistic simulations |
| url | http://www.sciencedirect.com/science/article/pii/S2590197425000229 |
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